Continuity mistake: When Kirk sits down to consult the computer, the big green potted plant on the shelf behind him is there in full shots and missing in close-ups. It's much too large to be completely hidden behind him: if it shows up behind his head in full shot, it should show in close-ups, too, but it doesn't. It's not there.

Continuity mistake: A subtle mistake, but when Spock is lying on the table in sick bay and recovers, the readings on the monitor are in the normal range. However Spock, as a Vulcan, produces very unusual readings on the monitors in other episodes.

Continuity mistake: At the end, Lt. Moreau gives Kirk a report to sign. After signing and giving it back, and after a dialog with Spock, he gets up, goes to Moreau, has the report and looks at it again.

Continuity mistake: As there were two screen used models of the Enterprise, when the ship is seen flipping from one universe to the other and back, the nacelles of the Imperial Enterprise have the solid red fronts with what appear to be antennae.

Trelane says he studied Earth images that travelled to him at light speed, and earlier they establish Gothos is 900 years from Earth. But Trelane references Napoleon and Hamilton, who weren't around until 1800 or so. That would put this episode in 2700, but the original Trek episodes are set in the 2200's.